Physics Test (Show your work by leaving calculations)
2/23/2001
Problems:
1. Define a vector quantity?
A quantity that requires both magnitude and direction for a complete description
2. What is a scalar quantity?
A quantity that is completely described by magnitude only
3. What is a vector?
A line in space that has a beginning and ending point with direction
4. An airplane is flying southwest at 120km/h relative to the surrounding air. A tailwind is
blowing southwest at a velocity of 15km/h. What is the resulting velocity relative to
the ground? Give answer and explain. Calculations not needed.
135km/h because the tailwind and airplane are traveling in the same direction the
resulting velocity is the sum of the two
5. An airplane is flying south at 140km/h relative to the surrounding air. A tailwind is
blowing north at a velocity of 20km/h. What is the resulting velocity relative to the
ground? Give answer and explain. Calculations not needed.
120km/h because the tailwind and airplane are traveling in opposite directions the
resulting velocity is the subtraction of the two
6. An airplane is caught in a strong crosswind of 120km/h traveling north. The airplane
encounters a crosswind of 30 km/h blowing from east to west. Will the airplane fly
faster or slower than 120 km/h and will it stay on course? Show calculations and
formula to verify your answer. Show calculations and formula? What is the
mathematical name of the formula used to solve the resultant?
A crosswind would increase the speed of the airplane and blow it off course by a
predictable amount. The plane will increase its velocity to an approximate sum of
123.69 as shown below.
resultant² = (30km/h)² + (120km/h)²
= 900 (km/h)² + 14400 (km/h)²
= 15300 (km/h)²
≈ 123.69 km/h
Pythagorean Theorem
7. What are the components of a vector?
Vertical and horizontal component of velocity
8. What is the process of determining the components of a vector called?
Resolution
9. At the instant a horizontally held rifle is fired, a bullet held at the rifle’s side is released
and drops on the ground. Which bullet strikes the ground first, the one fired from the
rifle or the one dropped? Explain in detail.
Both bullets fall at the same time with the same acceleration g and therefore strike the
ground at the same time.
10. A projectile is shot at an angle into the air. Neglecting air resistance, what is its
vertical acceleration? Its horizontal acceleration? Give answer and explain.
Calculations not needed.
Its vertical acceleration is g because the force of gravity is downward. Its horizontal
acceleration is zero because no horizontal force acts on it.
11. At what point in the path of a projectile relative to the ground does it have a minimum
speed? Explain in detail and think of its vector components.
The minimum speed of the projectile occurs at the top of its path. If it is launched
vertically, its speed at the top is zero. If it is projected at an angle, the vertical
component of the velocity is still zero at the top, leaving only the horizontal
component. So the speed at the top is equal to the horizontal component of the
projectile’s velocity at any point.
12. A person stands on the beach 5m above the water and throws a flat pebble 20m into
the waves. At what speed is the pebble thrown? Show calculations and formulas.
Rely on your previous knowledge to determine time.
Time is not given in the problem. We need to rely on former knowledge about gravity
applying to an object falling at a distance of 5m per second using d = ½ gt².
Therefore the speed must be 20m per second because the pebble travels 20m
according to gravity in one second.
13. Explain how a satellite falls to the earth? In other words, how does in fall or what
direction?
The satellite falls around the earth rather than into it
14. Calculate the resultant velocity of an airplane that normally flies at 200 km/h if it
encounters a 50-km/h tailwind. If it encounters a 50-km/h headwind? Show
calculations and formula to verify your answer.
250km/h because the tailwind and airplane are traveling in the same direction the
resulting velocity is the sum of the two
150km/h because the tailwind and airplane are traveling in opposite directions the
resulting velocity is the subtraction of the two
15. Calculate the magnitude of the resultant of a pair of 100-km/h velocity vectors that are
at right angles to each other? Show calculations and formula to verify your answer.
resultant² = (100km/h)² + (100km/h)²
= 10000 (km/h)² + 10000 (km/h)²
= 20000 (km/h)²
≈ 141.4 km/h